More than 4,000 current and former NYPD sergeants will have extra to celebrate this New Year’s — payouts for unpaid overtime as part of a $20 million lawsuit settlement.

“We’re expecting the checks to go out in the beginning of January and again in the spring,” said Edward Mullins, president of the Sergeants Benevolent Association.

The 4,302 claimants will be cut checks as high as $10,000 for up to a decade of unpaid overtime.

“We expect the checks to average out at about $6,000 each,” he said.

Mullins was the lead plaintiff in the 2004 federal lawsuit, which challenged the city’s refusal to pay NYPD sergeants overtime since 2002 for routine clerical functions before or after their shifts — such as conducting roll call or handling paperwork for arrests made by cops under their command.

“We were basically working either pre-tour or post-tour and not being allowed to put in for the overtime. We were doing all of this for many years without being compensated,” Mullins said.

Although some sergeants were never compensated for the additional hours, others were told to take it as “comp time.”

But some of these sergeants were denied requests to use that time because of staffing shortages.

Others who tried to collect compensation for the comp time at retirement found out that civil-service rules cap at 480 hours the maximum amount the city will pay out at retirement — and they were denied the extra money.

The hotly contested case — which included allegations that Internal Affairs detectives intimidated sergeants before their depositions about abuses — was settled in August. But it wasn’t until Thursday that Manhattan federal court Judge Shira Scheindlin signed off on the agreement.

Mullins noted that the first of the checks going out in January will represent a partial settlement representing the unpaid overtime wages, a sum that will be taxable.

A second check — to be mailed out sometime in the spring — will cover a damage settlement for the city’s failure to pay out the original overtime, monies that will not be taxable.

The $20 million payout Scheindlin endorsed does not address a similar lawsuit involving approximately 2,700 other NYPD sergeants who insist that they, too, were not paid overtime since 2006.

That case is still pending.

The city has been involved in settlement discussions, but no agreement has been reached.

“We’re not there yet,” insisted Mullins.

NYPD sergeant overtime settlement:

* The city will pay out $20 million to settle a lawsuit brought by the sergeants union seeking back overtime from 2002-2011.

* Checks for unpaid overtime earnings totaling $14 million will begin going out in January.

* Additional checks representing $6 million in damages for failing to pay the overtime will be sent out in the spring.

* There are 4,302 current and former sergeants who will be compensated.

* Approximately 2,700 additional current and former NYPD sergeants are part of another pending federal lawsuit charging they, too, weren’t paid overtime since 2006.